A214429 - OEIS

A214429

Integers of the form (n^2 - 49) / 120.

0, 1, 2, 4, 11, 15, 18, 23, 37, 44, 49, 57, 78, 88, 95, 106, 134, 147, 156, 170, 205, 221, 232, 249, 291, 310, 323, 343, 392, 414, 429, 452, 508, 533, 550, 576, 639, 667, 686, 715, 785, 816, 837, 869, 946, 980, 1003, 1038, 1122, 1159, 1184, 1222, 1313, 1353

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OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).

FORMULA

G.f.: x * (1 + x + 2*x^2 + 7*x^3 + 2*x^4 + x^5 + x^6) / ((1 - x) * (1 - x^4)^2).

a(n) = 2*a(n-4) - a(n-8) + 15 = a(-1 - n).

MATHEMATICA

CoefficientList[Series[x*(1+x+2*x^2+7*x^3+2*x^4+x^5+x^6)/((1-x)*(1- x^4)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 10 2018 *)

Select[(Range[0, 500]^2-49)/120, IntegerQ] (* or *) LinearRecurrence[ {1, 0, 0, 2, -2, 0, 0, -1, 1}, {0, 1, 2, 4, 11, 15, 18, 23, 37}, 80] (* Harvey P. Dale, Oct 23 2019 *)

PROG

(PARI) {a(n) = (((n*3 + 1) \ 4 * 10 + 5 + 2*(-1)^n)^2 - 49) / 120 }

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x+2*x^2+7*x^3+2*x^4+x^5+x^6)/((1-x)*(1-x^4)^2))); // G. C. Greubel, Aug 10 2018

CROSSREFS

Cf. A093722.

Sequence in context: A295968 A038193 A227456 * A002382 A356478 A330856

Adjacent sequences: A214426 A214427 A214428 * A214430 A214431 A214432

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Jul 17 2012

STATUS

approved